This invention relates to a filtering apparatus and a filtering system and, more particularly to a filtering apparatus which cleans cutting oil used as coolant in a metal cutting process by a machining center such as a lathe or a milling machine, by separating curled cuttings from the cutting oil with a conveyor having a hinge belt, and a filtering system which enables recycling of the cutting oil by fine filtration, with a combination of the hinge-belt type filtering apparatus and a filtering apparatus using a drum filter.